On the breakdown of acceleration waves in dissociating gas flows

The present paper is devoted to the study of characteristic solution in the neighbourhood of the leading frozen characteristics in dissociating gas flows. It is found that at the cusp of the envelope of intersecting forward characteristics there occurs a breakdown of the wave after a finite critical timet _o. It is observed that there exists a critical value of the initial amplitude of the wave such that all compressive waves with an initial amplitude greater than the critical one will terminate into a shock wave due to non-linear steepening while an initial amplitude less than the critical one will result in a continuous decay. It is also concluded that the breakdown point moves forward along the leading characteristics due to dissociation effects.